Micro-electromechanical systems (MEMS) sensors are widely used in consumer and industrial devices. Accelerometers, pressure sensors, and gyroscopes are three types of commonly deployed MEMS sensors. The small size and durability of MEMS sensors enable incorporation of these sensors into mobile electronic devices, automotive and aerospace applications, robotics, cameras, and a wide range of other electronic and electromechanical devices.
FIG. 6 depicts a prior art MEMS accelerometer 600 that includes a proof mass 604, an electronic detection and force feedback circuit 608 and force feedback electrodes 624A and 624B. During operation, a physical input force produces acceleration along the axis 532 that displaces the proof mass 604. During operation of the accelerometer 600, a force feedback circuit maintains the proof mass to a predetermined position (e.g. centered with the extension 606 equidistant between sensing electrodes 620A and 620B) when the accelerometer 600 experiences an acceleration. The force feedback from the feedback loop prevents substantial deflection of the proof mass 604 from the predetermined position, and the acceleration can be measured from changes in the level of force feedback that maintains the position of the proof mass.
The application of force feedback is known to the art to improve the linearity, gain, and dynamic range of the sensed acceleration in the accelerometer 600 since the force feedback signal ensures that deflection of the proof mass 604 only occurs over comparatively short distances and the proof mass 604 returns to the predetermined location much more quickly than would occur otherwise due to the inherent physical damping of the proof mass. The force feedback system detects small deflections in the position of the proof mass 604 as an error signal, and reduces or eliminates the error signal to maintain the position of the proof mass while the accelerometer 600 is under different levels of acceleration. In the accelerometer 600, the sensing electrodes 620A and 620B detect a differential capacitance level when the proof mass extension 606 deflects from a predetermined location in response to a physical acceleration, and the differential capacitance level acts as the error input for the feedback system. While FIG. 6 depicts a separate set of sensing electrodes 620A and 620B for illustrative purposes, in alternative embodiments the differential capacitance is measured in response to movement of the extension 607 between the feedback electrodes 624A and 624B.
During stable operation, the force feedback loop applies a force of equal magnitude and opposite direction to the proof mass 604 that cancels an external physical force that is applied to the accelerometer 600. The electronic circuit 608 includes a force feedback circuit that produces an electrical feedback signal for feedback electrodes 624A and 624B. The feedback electrodes 624A and 624B receive an electric charge that exerts a force on the proof mass 604 through an extension 607 to maintain the predetermined position of the proof mass 604 during acceleration of the sensor 600.
One issue with force feedback circuits is that the force feedback loop can become unstable, which produces an undesirable oscillation in the proof mass 604 instead of maintaining the predetermined location of the proof mass 604. FIG. 7 depicts Bode plots of gain and phase in a feedback loop in both stable and unstable regions. As is known in the art, the Bode stability criterion states that the phase shift around the force feedback loop must have a magnitude that is no more than −180° when the gain reaches unity (0 dB) for the feedback system to remain stable. To maintain stable operation in a practical circuit, the phase lag at 0 dB gain must have a magnitude that is smaller than −180° where the difference between the phase and −180° being referred to as the “phase margin.” For example, a −100° phase lag has a higher value than an unstable −180° phase lag but the −100° phase lag has a smaller magnitude (absolute value) than the −180° phase lag. The −100° phase lag has a phase margin of: −100°−(−180°)=80°. In many embodiments, a digital processor in the electronic circuit 608 is configured as a compensator that adjusts the feedback signal to maintain a phase margin that enables stable operation of the MEMS sensor. The compensator includes an analog to digital converter (ADC) that produces a digital output signal corresponding to the state of the error signal for the digital processor, and the output adjustments from the digital processor are provided to a digital to analog converter (DAC) that controls the output of the feedback signal to maintain the phase margin in the force feedback loop. While FIG. 6 depicts the accelerometer 600, similar force feedback circuits are used in a wide range of other MEMS devices including, but not limited to, gyroscopic sensors, micro-mirrors, and other transducers.
One drawback of existing digital compensator designs is that the digital control circuits require time to measure the feedback signal and generate a corresponding adjustment to maintain the phase margin for the feedback loop. The delay between receiving the feedback signal and generating the output signal contributes to the overall “phase lag.” FIG. 4 depicts phase lag in a timing diagram of a prior art digital compensator where the delay introduced by the ADC, digital computation in the digital processor, and DAC corresponds to an entire feedback and sense cycle in the accelerometer. Some prior art embodiments include even greater time delays than the delay that is depicted in FIG. 4. The phase lag due to the delay in processing the feedback signal increases the phase error in the force feedback signal. As depicted in the Bode plot of FIG. 8, the delay in the compensator increases the phase error towards the unstable −180° level at 0 dB gain, which reduces or eliminates the effectiveness of the compensator. Given the drawbacks in the existing digital compensator embodiments, improvements to the force feedback controls in MEMS sensors that improve the stability of force feedback loops would be beneficial.